Cheapest and easiest way to slow down a motor

[billbo911]

Originally Posted by sanddrag

Also, would anyone happen to know what is inside this box? Thanks.

I'd put money (only a couple bucks) on it containing a "chopper circuit". By using an SCR, or pair of SCR's, it will pass as little or as much of the full AC signal as you set the dial to. To understand how it operates really requires a little understanding of electronics and maybe a picture or two, but I'll try to describe it.
At full speed, the circuit allows the full positive and negative cycles of the AC to pass. When you turn down the speed dial, the circuit will only pass a equal portion of the positive and negative cycles.
Say you only want to provide the motor ~50% power, the circuit would pass 4.15 ms of the negative cycle as it approaches 0Vac and 4.15ms of the positive cycle as it moves away from 0Vac. This adds up to 8.3ms per cycle, half of the full 16.6ms normal AC cycle.
I really hope that helps. This again is where "A picture paints a thousand words" really is true.